{"id":218,"date":"2020-08-04T02:16:30","date_gmt":"2020-08-04T02:16:30","guid":{"rendered":"http:\/\/soulofmathematics.com\/?p=218"},"modified":"2020-08-04T03:10:20","modified_gmt":"2020-08-04T03:10:20","slug":"the-collatz-conjecture","status":"publish","type":"post","link":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/","title":{"rendered":"The Collatz Conjecture"},"content":{"rendered":"\n
\"\"
Collatz Conjecture Art<\/figcaption><\/figure>\n\n\n\n

Lets take a positive integer. <\/p>\n\n\n\n

If the chosen number is even then just divide it by 2.<\/strong><\/td>If the chosen number is odd triple it and add 1.<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Now keep applying these rules repeatedly. <\/p>\n\n\n\n

Statement<\/strong>:- This process will eventually reach the number 1, regardless of which positive integer is chosen initially.<\/em><\/p>\n\n\n\n

\n

In notation: \"\"<\/p>\n<\/div><\/div>\n\n\n\n

(that is:\u00a0ai<\/sub><\/em>\u00a0is the value of\u00a0f<\/em>\u00a0applied to\u00a0n<\/em>\u00a0recursively\u00a0i<\/em>\u00a0times;\u00a0ai<\/sub><\/em>\u00a0=\u00a0f<\/em>i<\/em><\/sup>(n<\/em>)).<\/p>\n\n\n\n

That smallest\u00a0i<\/em>\u00a0such that\u00a0ai<\/sub><\/em>\u00a0= 1\u00a0is called the\u00a0total stopping time<\/strong>\u00a0of\u00a0n<\/em>. The conjecture asserts that every\u00a0n<\/em>\u00a0has a well-defined total stopping time. If, for some\u00a0n<\/em>, such an\u00a0i<\/em>\u00a0doesn’t exist, we say that\u00a0n<\/em>\u00a0has infinite total stopping time and the conjecture is false. If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1, or increase without bound. No such sequence has been found.<\/p>\n\n\n\n

For example starting with 12 we get the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1.<\/p>\n\n\n\n

The sequence of numbers involved is sometimes referred to as the\u00a0hailstone sequence<\/strong>\u00a0or\u00a0hailstone numbers<\/strong>\u00a0(because the values are usually subject to multiple descents and ascents like\u00a0hailstones<\/a>\u00a0in a cloud),\u00a0or as\u00a0wondrous numbers<\/strong>.<\/p>\n\n\n\n

\u00a0“Mathematics may not be ready for such problems.”- Paul Erd\u0151s<\/a><\/h4>\n\n\n\n
\"\"
All Returns To 1<\/figcaption><\/figure>\n\n\n\n

Defining the\u00a0Collatz function<\/em>\u00a0f(x) as follows:<\/p>\n\n\n\n

\"\"<\/figure>
\n

If x is a positive integer, then f(x) is the next number after x in its Collatz sequence.<\/p>\n<\/div><\/div>\n\n\n\n

To extend this function to the real numbers, simply recall that (-1)x<\/sup>\u00a0= cos(\u03c0x). In fact, this gets us an extension to the complex numbers at the same time, and after some simplification we arrive at:<\/p>\n\n\n\n

\"\"<\/figure>
\n

It is a holomorphic function and we can study the fractal that its iterates induce.<\/p>\n<\/div><\/div>\n\n\n\n

\"\"
Collatz Fractals<\/figcaption><\/figure>\n\n\n\n

The fractal is located on the complex plane, and the horizontal line through the middle of the image is the real line. Black regions are regions in which the orbit of that number is bounded, while other colors indicate that the orbit of that number is unbounded (notice the large region of bounded numbers around z = 0). The big \u201cspikes\u201d that occur along the real line are, as we would expect, located at the integers (the image above is wide enough that you can see the spikes at z = -2, -1, 1, and 2).<\/p>\n\n\n\n

The Collatz Conjecture is quite intimately connected with deep roots of nature and much more lies in the dark left to discovered about it which includes a PROOF.<\/h6>\n\n\n\n
\n
All Posts<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Lets take a positive integer. If the chosen number is even then just divide it by 2. If the chosen number is odd triple it and add 1. Now keep applying these rules repeatedly. Statement:- This process will eventually reach the number 1, regardless of which positive integer is chosen initially. In notation: (that is:\u00a0ai\u00a0is the value of\u00a0f\u00a0applied to\u00a0n\u00a0recursively\u00a0i\u00a0times;\u00a0ai\u00a0=\u00a0fi(n)). That smallest\u00a0i\u00a0such that\u00a0ai\u00a0= 1\u00a0is called the\u00a0total stopping time\u00a0of\u00a0n. The conjecture asserts that every\u00a0n\u00a0has a well-defined total stopping time. If, for some\u00a0n, such an\u00a0i\u00a0doesn’t exist, we say that\u00a0n\u00a0has infinite total stopping time and the conjecture is false. If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1, or increase without bound. No such sequence has been found. For example starting with 12 we get the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1. The sequence of numbers involved is sometimes referred to as the\u00a0hailstone sequence\u00a0or\u00a0hailstone numbers\u00a0(because the values are usually subject to multiple descents and ascents like\u00a0hailstones\u00a0in a cloud),\u00a0or as\u00a0wondrous numbers. \u00a0“Mathematics may not be ready for such problems.”- Paul Erd\u0151s Defining the\u00a0Collatz function\u00a0f(x) as follows: If x is a positive integer, then f(x) is the next number after x in its Collatz sequence. To extend this function to the real numbers, simply recall that (-1)x\u00a0= cos(\u03c0x). In fact, this gets us an extension to the complex numbers at the same time, and after some simplification we arrive at: It is a holomorphic function and we can study the fractal that its iterates induce. The fractal is located on the complex plane, and the horizontal line through the middle of the image is the real line. Black regions are regions in which the orbit of that number is bounded, while other colors indicate that the orbit of that number is unbounded (notice the large region of bounded numbers around z = 0). The big \u201cspikes\u201d that occur along the real line are, as we would expect, located at the integers (the image above is wide enough that you can see the spikes at z = -2, -1, 1, and 2). The Collatz Conjecture is quite intimately connected with deep roots of nature and much more lies in the dark left to discovered about it which includes a PROOF.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-218","post","type-post","status-publish","format-standard","hentry","category-sneak-peeks"],"featured_image_src":"","blog_images":{"medium":"","large":""},"ams_acf":[],"yoast_head":"\nThe Collatz Conjecture - SOUL OF MATHEMATICS<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Collatz Conjecture - SOUL OF MATHEMATICS\" \/>\n<meta property=\"og:description\" content=\"Lets take a positive integer. If the chosen number is even then just divide it by 2. If the chosen number is odd triple it and add 1. Now keep applying these rules repeatedly. Statement:- This process will eventually reach the number 1, regardless of which positive integer is chosen initially. In notation: (that is:\u00a0ai\u00a0is the value of\u00a0f\u00a0applied to\u00a0n\u00a0recursively\u00a0i\u00a0times;\u00a0ai\u00a0=\u00a0fi(n)). That smallest\u00a0i\u00a0such that\u00a0ai\u00a0= 1\u00a0is called the\u00a0total stopping time\u00a0of\u00a0n. The conjecture asserts that every\u00a0n\u00a0has a well-defined total stopping time. If, for some\u00a0n, such an\u00a0i\u00a0doesn’t exist, we say that\u00a0n\u00a0has infinite total stopping time and the conjecture is false. If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1, or increase without bound. No such sequence has been found. For example starting with 12 we get the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1. The sequence of numbers involved is sometimes referred to as the\u00a0hailstone sequence\u00a0or\u00a0hailstone numbers\u00a0(because the values are usually subject to multiple descents and ascents like\u00a0hailstones\u00a0in a cloud),\u00a0or as\u00a0wondrous numbers. \u00a0“Mathematics may not be ready for such problems.”- Paul Erd\u0151s Defining the\u00a0Collatz function\u00a0f(x) as follows: If x is a positive integer, then f(x) is the next number after x in its Collatz sequence. To extend this function to the real numbers, simply recall that (-1)x\u00a0= cos(\u03c0x). In fact, this gets us an extension to the complex numbers at the same time, and after some simplification we arrive at: It is a holomorphic function and we can study the fractal that its iterates induce. The fractal is located on the complex plane, and the horizontal line through the middle of the image is the real line. Black regions are regions in which the orbit of that number is bounded, while other colors indicate that the orbit of that number is unbounded (notice the large region of bounded numbers around z = 0). The big \u201cspikes\u201d that occur along the real line are, as we would expect, located at the integers (the image above is wide enough that you can see the spikes at z = -2, -1, 1, and 2). The Collatz Conjecture is quite intimately connected with deep roots of nature and much more lies in the dark left to discovered about it which includes a PROOF.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/\" \/>\n<meta property=\"og:site_name\" content=\"SOUL OF MATHEMATICS\" \/>\n<meta property=\"article:published_time\" content=\"2020-08-04T02:16:30+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-08-04T03:10:20+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg\" \/>\n<meta name=\"author\" content=\"Rajarshi Dey\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Rajarshi Dey\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/\",\"url\":\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/\",\"name\":\"The Collatz Conjecture - SOUL OF MATHEMATICS\",\"isPartOf\":{\"@id\":\"https:\/\/soulofmathematics.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg\",\"datePublished\":\"2020-08-04T02:16:30+00:00\",\"dateModified\":\"2020-08-04T03:10:20+00:00\",\"author\":{\"@id\":\"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c\"},\"breadcrumb\":{\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#primaryimage\",\"url\":\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg?fit=930%2C701&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg?fit=930%2C701&ssl=1\",\"width\":930,\"height\":701},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/soulofmathematics.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"The Collatz Conjecture\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/soulofmathematics.com\/#website\",\"url\":\"https:\/\/soulofmathematics.com\/\",\"name\":\"SOUL OF MATHEMATICS\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/soulofmathematics.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c\",\"name\":\"Rajarshi Dey\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/soulofmathematics.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g\",\"caption\":\"Rajarshi Dey\"},\"sameAs\":[\"http:\/\/soulofmathematics.com\"],\"url\":\"https:\/\/soulofmathematics.com\/index.php\/author\/rajarshidey1729gmail-com\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The Collatz Conjecture - SOUL OF MATHEMATICS","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/","og_locale":"en_US","og_type":"article","og_title":"The Collatz Conjecture - SOUL OF MATHEMATICS","og_description":"Lets take a positive integer. If the chosen number is even then just divide it by 2. If the chosen number is odd triple it and add 1. Now keep applying these rules repeatedly. Statement:- This process will eventually reach the number 1, regardless of which positive integer is chosen initially. In notation: (that is:\u00a0ai\u00a0is the value of\u00a0f\u00a0applied to\u00a0n\u00a0recursively\u00a0i\u00a0times;\u00a0ai\u00a0=\u00a0fi(n)). That smallest\u00a0i\u00a0such that\u00a0ai\u00a0= 1\u00a0is called the\u00a0total stopping time\u00a0of\u00a0n. The conjecture asserts that every\u00a0n\u00a0has a well-defined total stopping time. If, for some\u00a0n, such an\u00a0i\u00a0doesn’t exist, we say that\u00a0n\u00a0has infinite total stopping time and the conjecture is false. If the conjecture is false, it can only be because there is some starting number which gives rise to a sequence that does not contain 1. Such a sequence would either enter a repeating cycle that excludes 1, or increase without bound. No such sequence has been found. For example starting with 12 we get the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1. The sequence of numbers involved is sometimes referred to as the\u00a0hailstone sequence\u00a0or\u00a0hailstone numbers\u00a0(because the values are usually subject to multiple descents and ascents like\u00a0hailstones\u00a0in a cloud),\u00a0or as\u00a0wondrous numbers. \u00a0“Mathematics may not be ready for such problems.”- Paul Erd\u0151s Defining the\u00a0Collatz function\u00a0f(x) as follows: If x is a positive integer, then f(x) is the next number after x in its Collatz sequence. To extend this function to the real numbers, simply recall that (-1)x\u00a0= cos(\u03c0x). In fact, this gets us an extension to the complex numbers at the same time, and after some simplification we arrive at: It is a holomorphic function and we can study the fractal that its iterates induce. The fractal is located on the complex plane, and the horizontal line through the middle of the image is the real line. Black regions are regions in which the orbit of that number is bounded, while other colors indicate that the orbit of that number is unbounded (notice the large region of bounded numbers around z = 0). The big \u201cspikes\u201d that occur along the real line are, as we would expect, located at the integers (the image above is wide enough that you can see the spikes at z = -2, -1, 1, and 2). The Collatz Conjecture is quite intimately connected with deep roots of nature and much more lies in the dark left to discovered about it which includes a PROOF.","og_url":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/","og_site_name":"SOUL OF MATHEMATICS","article_published_time":"2020-08-04T02:16:30+00:00","article_modified_time":"2020-08-04T03:10:20+00:00","og_image":[{"url":"https:\/\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg"}],"author":"Rajarshi Dey","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Rajarshi Dey","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/","url":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/","name":"The Collatz Conjecture - SOUL OF MATHEMATICS","isPartOf":{"@id":"https:\/\/soulofmathematics.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#primaryimage"},"image":{"@id":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#primaryimage"},"thumbnailUrl":"https:\/\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg","datePublished":"2020-08-04T02:16:30+00:00","dateModified":"2020-08-04T03:10:20+00:00","author":{"@id":"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c"},"breadcrumb":{"@id":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#primaryimage","url":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg?fit=930%2C701&ssl=1","contentUrl":"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2020\/08\/collatzconjecture-1.jpg?fit=930%2C701&ssl=1","width":930,"height":701},{"@type":"BreadcrumbList","@id":"https:\/\/soulofmathematics.com\/index.php\/the-collatz-conjecture\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/soulofmathematics.com\/"},{"@type":"ListItem","position":2,"name":"The Collatz Conjecture"}]},{"@type":"WebSite","@id":"https:\/\/soulofmathematics.com\/#website","url":"https:\/\/soulofmathematics.com\/","name":"SOUL OF MATHEMATICS","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/soulofmathematics.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/soulofmathematics.com\/#\/schema\/person\/c61ee309ed66bc94ba7a27f6129b945c","name":"Rajarshi Dey","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/soulofmathematics.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/14acfcec71e13078f5b322bb6adfd1f6579c091317d0e0077c2311511263a8b0?s=96&d=mm&r=g","caption":"Rajarshi Dey"},"sameAs":["http:\/\/soulofmathematics.com"],"url":"https:\/\/soulofmathematics.com\/index.php\/author\/rajarshidey1729gmail-com\/"}]}},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","jetpack-related-posts":[],"jetpack_shortlink":"https:\/\/wp.me\/pcfs4y-3w","_links":{"self":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/posts\/218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/comments?post=218"}],"version-history":[{"count":0,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/posts\/218\/revisions"}],"wp:attachment":[{"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/media?parent=218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/categories?post=218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/soulofmathematics.com\/index.php\/wp-json\/wp\/v2\/tags?post=218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}